{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:1991:JKTY5FUAXSZSDVQQ5MLPJTUTXC","short_pith_number":"pith:JKTY5FUA","canonical_record":{"source":{"id":"math/9201295","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1991-10-11T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"214eb9d7b3b38936f4bc29495a091885de11de0aef1e3e98a543ac8215adb313","abstract_canon_sha256":"e9f6686bf27f6326c41805d8cf01809bd297ec39ad93a3097f7c9b00e01db340"},"schema_version":"1.0"},"canonical_sha256":"4aa78e9680bcb321d610eb16f4ce93b8a164986939a273adec7bac31ba154d0c","source":{"kind":"arxiv","id":"math/9201295","version":1},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9201295","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/9201295v1","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9201295","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"JKTY5FUAXSZS","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"JKTY5FUAXSZSDVQQ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"JKTY5FUA","created_at":"2026-05-18T12:25:47Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:1991:JKTY5FUAXSZSDVQQ5MLPJTUTXC","target":"record","payload":{"canonical_record":{"source":{"id":"math/9201295","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.DS","submitted_at":"1991-10-11T00:00:00Z","cross_cats_sorted":[],"title_canon_sha256":"214eb9d7b3b38936f4bc29495a091885de11de0aef1e3e98a543ac8215adb313","abstract_canon_sha256":"e9f6686bf27f6326c41805d8cf01809bd297ec39ad93a3097f7c9b00e01db340"},"schema_version":"1.0"},"canonical_sha256":"4aa78e9680bcb321d610eb16f4ce93b8a164986939a273adec7bac31ba154d0c","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:54.512205Z","signature_b64":"tFVhw9Nvx6HzZx0Lw4MIYzbOh0RSfaA6Mlzl2zPuONq8bBsKEVxo/2FIqTyy4j2bp1aS6az8/XapdDPzeqU9Bg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"4aa78e9680bcb321d610eb16f4ce93b8a164986939a273adec7bac31ba154d0c","last_reissued_at":"2026-05-18T01:05:54.511775Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:54.511775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"math/9201295","source_version":1,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Qo7ouYJGcSRvAiiGpHGFiUYp21rut/9IsP1Nl3weo/g96irQBJDGyPwYy+xOAn213iJmRShmQ65Gff3/BQcUDw==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T19:40:05.033254Z"},"content_sha256":"1cf95a9aea78a7b4d2d871ef5e73678f1d8e8abef53a85abb8746ace08097395","schema_version":"1.0","event_id":"sha256:1cf95a9aea78a7b4d2d871ef5e73678f1d8e8abef53a85abb8746ace08097395"},{"event_type":"graph_snapshot","subject_pith_number":"pith:1991:JKTY5FUAXSZSDVQQ5MLPJTUTXC","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"On the quasisymmetrical classification of infinitely renormalizable maps: II. remarks on maps with a bounded type topology.","license":"","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Yunping Jiang","submitted_at":"1991-10-11T00:00:00Z","abstract_excerpt":"We use the upper and lower potential functions and Bowen's formula estimating the Hausdorff dimension of the limit set of a regular semigroup generated by finitely many $C^{1+\\alpha}$-contracting mappings. This result is an application of the geometric distortion lemma in the first paper at this series."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201295","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T01:05:54Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"CJrrjtkC//vrKh9+aGv2OmyRSIniqJKuMj0xX8Drm1Ho4NcqfB+SjwvCrUCM4boVqjEcDONfApARoOtbbKlVCA==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-30T19:40:05.033615Z"},"content_sha256":"6a3c5cfab175770034976ca6965911a2fb96cbb38c82cfc84b003a551aa8c675","schema_version":"1.0","event_id":"sha256:6a3c5cfab175770034976ca6965911a2fb96cbb38c82cfc84b003a551aa8c675"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/JKTY5FUAXSZSDVQQ5MLPJTUTXC/bundle.json","state_url":"https://pith.science/pith/JKTY5FUAXSZSDVQQ5MLPJTUTXC/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/JKTY5FUAXSZSDVQQ5MLPJTUTXC/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-30T19:40:05Z","links":{"resolver":"https://pith.science/pith/JKTY5FUAXSZSDVQQ5MLPJTUTXC","bundle":"https://pith.science/pith/JKTY5FUAXSZSDVQQ5MLPJTUTXC/bundle.json","state":"https://pith.science/pith/JKTY5FUAXSZSDVQQ5MLPJTUTXC/state.json","well_known_bundle":"https://pith.science/.well-known/pith/JKTY5FUAXSZSDVQQ5MLPJTUTXC/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:1991:JKTY5FUAXSZSDVQQ5MLPJTUTXC","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"e9f6686bf27f6326c41805d8cf01809bd297ec39ad93a3097f7c9b00e01db340","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1991-10-11T00:00:00Z","title_canon_sha256":"214eb9d7b3b38936f4bc29495a091885de11de0aef1e3e98a543ac8215adb313"},"schema_version":"1.0","source":{"id":"math/9201295","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"math/9201295","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"arxiv_version","alias_value":"math/9201295v1","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9201295","created_at":"2026-05-18T01:05:54Z"},{"alias_kind":"pith_short_12","alias_value":"JKTY5FUAXSZS","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_16","alias_value":"JKTY5FUAXSZSDVQQ","created_at":"2026-05-18T12:25:47Z"},{"alias_kind":"pith_short_8","alias_value":"JKTY5FUA","created_at":"2026-05-18T12:25:47Z"}],"graph_snapshots":[{"event_id":"sha256:6a3c5cfab175770034976ca6965911a2fb96cbb38c82cfc84b003a551aa8c675","target":"graph","created_at":"2026-05-18T01:05:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We use the upper and lower potential functions and Bowen's formula estimating the Hausdorff dimension of the limit set of a regular semigroup generated by finitely many $C^{1+\\alpha}$-contracting mappings. This result is an application of the geometric distortion lemma in the first paper at this series.","authors_text":"Yunping Jiang","cross_cats":[],"headline":"","license":"","primary_cat":"math.DS","submitted_at":"1991-10-11T00:00:00Z","title":"On the quasisymmetrical classification of infinitely renormalizable maps: II. remarks on maps with a bounded type topology."},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9201295","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:1cf95a9aea78a7b4d2d871ef5e73678f1d8e8abef53a85abb8746ace08097395","target":"record","created_at":"2026-05-18T01:05:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"e9f6686bf27f6326c41805d8cf01809bd297ec39ad93a3097f7c9b00e01db340","cross_cats_sorted":[],"license":"","primary_cat":"math.DS","submitted_at":"1991-10-11T00:00:00Z","title_canon_sha256":"214eb9d7b3b38936f4bc29495a091885de11de0aef1e3e98a543ac8215adb313"},"schema_version":"1.0","source":{"id":"math/9201295","kind":"arxiv","version":1}},"canonical_sha256":"4aa78e9680bcb321d610eb16f4ce93b8a164986939a273adec7bac31ba154d0c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"4aa78e9680bcb321d610eb16f4ce93b8a164986939a273adec7bac31ba154d0c","first_computed_at":"2026-05-18T01:05:54.511775Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:05:54.511775Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tFVhw9Nvx6HzZx0Lw4MIYzbOh0RSfaA6Mlzl2zPuONq8bBsKEVxo/2FIqTyy4j2bp1aS6az8/XapdDPzeqU9Bg==","signature_status":"signed_v1","signed_at":"2026-05-18T01:05:54.512205Z","signed_message":"canonical_sha256_bytes"},"source_id":"math/9201295","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1cf95a9aea78a7b4d2d871ef5e73678f1d8e8abef53a85abb8746ace08097395","sha256:6a3c5cfab175770034976ca6965911a2fb96cbb38c82cfc84b003a551aa8c675"],"state_sha256":"be371411b6f81aa599d9998909ea88542ae49d404521e516f420e3042bda1719"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"na1i9/ifztXw/LjDeJsmmRNICdTrjKV7rKygcdGOrF/PO3jvn1NXaljs/Vwak2Un/tE9j1oP3wbvl1QKxSmpAQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-30T19:40:05.035542Z","bundle_sha256":"07a0ef4eb95af9ee53a10217af90d90c935b319ba20608ea448fb8453f190f8e"}}